Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


Multiplicative bijections of semigroups of interval-valued continuous functions

Author: Jesús Araujo
Journal: Proc. Amer. Math. Soc. 137 (2009), 171-178
MSC (2000): Primary 46J10; Secondary 46E05, 54D35.
Published electronically: July 1, 2008
MathSciNet review: 2439438
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We characterize all compact and Hausdorff spaces $ X$ which satisfy the condition that for every multiplicative bijection $ \varphi$ on $ C(X, I)$, there exist a homeomorphism $ \mu : X \longrightarrow X$ and a continuous map $ p: X \longrightarrow (0, +\infty)$ such that

$\displaystyle \varphi (f) (x) = f(\mu (x))^{p(x)}$

for every $ f \in C(X,I)$ and $ x \in X$. This allows us to disprove a conjecture of Marovt (Proc. Amer. Math. Soc. 134 (2006), 1065-1075). Some related results on other semigroups of functions are also given.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 46J10, 46E05, 54D35.

Retrieve articles in all journals with MSC (2000): 46J10, 46E05, 54D35.

Additional Information

Jesús Araujo
Affiliation: Departamento de Matemáticas, Estadística y Computación, Universidad de Cantabria, Facultad de Ciencias, Avda. de los Castros, s. n., E-39071 Santander, Spain

PII: S 0002-9939(08)09448-3
Received by editor(s): October 26, 2007
Received by editor(s) in revised form: December 10, 2007
Published electronically: July 1, 2008
Additional Notes: This research was partially supported by the Spanish Ministry of Science and Education (Grant number MTM2006-14786).
Communicated by: N. Tomczak-Jaegermann
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia